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mestny [16]
3 years ago
14

Number 13a and 13b, please.

Mathematics
1 answer:
vova2212 [387]3 years ago
3 0
Both are true.
a) The box dimensions in terms of cube size are 12 x 1 x 5. The product of these is 60.

b) The product of box dimensions is 6 x (1/2) x (2 1/2) = 3 x (2 1/2) = 7 1/2 units³.
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What is 9 over 10 + 15 over 40
Alex_Xolod [135]
9     15                        *The denominator must be the same.  9      4      36
--- + ---- =                                                                                 --- × --- = ----
10    40                                                                                    10     4     40
36   15     51               *Then simplify.
--- + --- = ----
40    40    40
51       11                    * This the answer
--- = 1 --- 
40       40


5 0
3 years ago
A scientist needs 10 L of a solution that is 60% acid. She has a 50% acid solution and a 90% acid solution she can mix together
sineoko [7]

Answer:

<u>The equations system is:</u>

<u>x + y = 10</u>

<u>0.5x + 0.9y = 6</u>

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Liters of 60% acid solution needed = 10

x = Number of liters of the 50% solution

y = Number of liters of the 90% solution

2. Which equation represents the total liters of acid that are needed?

There are two equations needed:

The first one related to the total liters needed, 10 in this case:

x + y = 10

The second one related to the acid concentration of the 10 liters:

0.5x + 0.9y = 10 * 0.6

0.5x + 0.9y = 6

<u>The equations system is:</u>

<u>x + y = 10</u>

<u>0.5x + 0.9y = 6</u>

Solving for x and y in the 2nd equation, we have:

0.5 (10 - y) + 0.9y = 6

5 - 0.5y + 0.9y = 6

0.4y = 6 - 5

0.4y = 1

y = 1/0.4 = 2.5 ⇒ x = 7.5 (10 - 2.5)

The scientist can mix 7.5 liters of the 50% acid solution and 2.5 liters of the 90% acid solution to get the 10 liters of the 60% acid solution.

6 0
4 years ago
Please help me out thank you so much :) <br> 7+7
Sindrei [870]
7+7=14

Hope this helps!! <3
7 0
3 years ago
Read 2 more answers
The y-intercept of y=2.5^x-6
almond37 [142]

Answer:

-6

Step-by-step explanation:

-6 is the y-intercept :)

5 0
3 years ago
Find the angle between u = i+sqr of 7j and v = -i+9j. Round to the nearest tenth of a degree.
Zolol [24]

\bf ~~~~~~~~~~~~\textit{angle between two vectors } \\\\ cos(\theta)=\cfrac{\stackrel{\textit{dot product}}{u \cdot v}}{\stackrel{\textit{magnitude product}}{||u||~||v||}} \implies \measuredangle \theta = cos^{-1}\left(\cfrac{u \cdot v}{||u||~||v||}\right) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \begin{cases} u=i+\sqrt{7}j\implies &\\\\ v=-i+9j\implies & \end{cases} \\\\[-0.35em] ~\dotfill

\bf u\cdot v\implies (1)(-1)~+~(\sqrt{7})(9)\implies -1+9\sqrt{7}\implies 9\sqrt{7}-1~\hfill dot~product \\\\[-0.35em] ~\dotfill\\\\ ||u||\implies \sqrt{1^2+(\sqrt{7})^2}\implies \sqrt{1+7}\implies \sqrt{8}~\hfill magnitudes \\\\\\ ||v||\implies \sqrt{(-1)^2+9^2}\implies \sqrt{1+81}\implies \sqrt{82} \\\\[-0.35em] ~\dotfill

\bf \theta =cos^{-1}\left( \cfrac{9\sqrt{7}-1}{\sqrt{8}\cdot \sqrt{82}} \right)\implies \theta =cos^{-1}\left( \cfrac{9\sqrt{7}-1}{\sqrt{656}} \right) \\\\\\ \theta \approx cos^{-1}(0.8906496638868531)\implies \theta \approx 27.05

make sure your calculator is in Degree mode.

6 0
3 years ago
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